Question

For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is:

Options

• 20

• 10

• 15

• 30

Answer 1

20

Explanation:

Number of nuclei remaining, N = 600 − 450 = 150 after time ‘t’

`"N"/"N"_0 = 150/600 = 1/4`

N = N₀e^−λt ⇒ `ℓ"n""N"_0/"N" = λ"t"`

⇒ t = `1/λ ℓ"n""N"_0/"N"`

⇒ t = `(2.303 xx "T"_(1/2))/0.693 log_10  "N"_0/"N" = (2.303 xx 10)/0.693 log_10 4`